A huge number of articles have appeared in the media and the technical press regarding this new system. The Economist, for example, published an article in October 2015 entitled: “The Trust Machine: The Technology Behind bitcoin Could Transform How the Economy Works.” Such a transformation has not yet occurred, but the success of this particular cryptocurrency can be measured by the current value of its daily transactions: approximately US$74 billion in 2016 vs. US$18 billion in 2015.

Jean-Paul Delahaye’s article offers a detailed and precise survey of bitcoin’s history and its main technical aspects. How the system functions is, in itself, quite captivating, as it builds upon recent developments in theoretical computer science and cryptography. As clearly explained in the article, the two main technologies involved, digital tokens and blockchains, exploit the availability of cheap storage. On the other hand, a more detailed description of the proof of work system might have been useful.

I would like to stress here that the future prospects of bitcoin, and other similar applications, depend on overcoming scalability limitations, but most of all, on a complex mixture of technical, legal and societal factors which should be—and certainly are—the object of careful analysis by different interdisciplinary research groups.

The current power of the system is a direct consequence of the immense progress made in computing and the precipitous fall of the cost per terabyte of memory and storage. This makes it possible, in practical terms, to store each transaction within the bitcoin blockchain thousands of times. It is also a consequence of the pervasiveness of the internet.

Cryptocurrencies allow for free transactions (or quasi-free; some energy is spent by the so-called miners) in complete anonymity with respect to origin and destination. This anonymity was the object of criticism at the beginning, as it was thought to permit large exchanges of dirty money. But this argument quickly disappeared, even though over ninety percent of bitcoin transactions today involve China.

Future innovations will probably be found in the use of the system as a foundation for other applications. Still, some banks and centralized institutions are exploring the new technology and might use part of it. Some will likely resist adopting these technologies.

If the system develops further, it will have to confront difficult issues involved in mixing the crypto-world with the everyday world, as for example, in the case of taxes and inheritances. More generally, at some point, the law will have to become involved with contracts, which themselves rely on identity, property, and trust. Indeed, the whole classical legal system is based on the concept of identity. In the virtual world of cryptocurrencies, identity is a big issue. Currently the system is still evolving in relation to smart contracts.

Smart contracts are stored on the blockchain so that everyone can check and trust them. They can facilitate negotiation or the execution of an agreement (contract) via, of course, blockchain technology.

The process is automated and can be a substitute for legal contracts, which, in turn, raises other issues. The content of a smart contract is recorded in a computer language as a set of instructions. Contract tools define rules and consequences, stating obligations, benefits, and penalties, which can be automatically executed by a distributed ledger system.

The legal aspects of smart contract technology, in parallel and at odds with traditional legal practice and theory, are the object of intense scrutiny and study.

All the usual interpretational apparatus surrounding classical human legal contracts—expertise, arbitrage, tribunals, execution of contracts, and conflicts arising from their execution—go much further than even the sophisticated technology that ultimately reduces the process to a huge, but irreversible, algorithm.

There are more things in heaven and earth Than are dreamt of in your philosophy!

Deeper intellectual matters are also involved in these developments. How, for example, do you recognize a string of data as being original, as opposed to a copy? This issue is strikingly similar to philosophical issues that date back to the time of Aristotle, but which have reappeared with issues involving identity in set theory. They arose at the beginning of the twentieth century with the theory of types, created by Bertrand Russell to answer some antinomies of set theory, and have been revived recently with the revolutionary work of Vladimir Voevodsky.1

Voevodsky was originally motivated by the aim of constructing proof assistants and theorem provers. He was similarly motivated with respect to computer technology, as can be seen here with cryptotechnology, by the question of tracing identical, or isomorphic objects via software. This led him to Homotopy Type Theory, which is still in development.

The question of identity might play an important role in future applications. Tokens and blockchains may eventually become the foundations of many more applications beyond financial services: supply chain documentation, land registration, health records, and smart contracts, among myriads of intelligent devices.

In any case, there will be more and more developments that banks and centralized intitutions will have to confront, exploit, or compete with.

Regarding the future prospects of bitcoin, a prestigious group of consultants have offered a cautious assessment.2 An essential step is the development of interdisciplinary studies analyzing bitcoin from the perspectives of computer science, law, and economics. Also of great interest is the emergence of an exceptional situation in which decision making processes are shared between actors, or developers, and participants across the globe.

The future is not yet written!

Jean-Michel Kantor

Jean-Paul Delahayereplies:

Jean-Michel Kantor is correct in stating that the future of bitcoin and of blockchains

depend on overcoming scalability limitations, but most of all, on a complex mixture of technical, legal and societal factors which should be—and certainly are—the object of careful analysis by different interdisciplinary research groups.

It is fascinating that after eight years of existence, it remains difficult to predict with any degree of certainty what will happen and the future role this new technology will play as a method for issuing currency, as a tool for doing away with a trusted third party, or for simplifying other technologies. This is certainly not a passing fad, but the way in which all of this will express itself—in monetary, economic, social, or political terms—remains, for the most part, unclear.

I have a harder time understanding the connections the author of the letter seems to detect with homotopy type theory, which is an attempt to formulate an alternative basis for mathematics, separate from set theory and the usual axiomatic, based on ZFC. The problem of chain identity in computer science and in cryptography is not really that difficult, since the chain components are elements that are easy to identify within a finite group of shared codes. Perhaps I have not understood what Kantor means to say on this point.

Translated from the French by the editors.

Jean-Michel Kantor is a mathematician at the Institut de Mathématiques de Jussieu in Paris.

Jean-Paul Delahaye is a mathematician and professor emeritus in computer science at the University of Lille.